no. 2
A generalization of the sizes of differential equations and its applications to G-function theory
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 30 (2001) no. 2, pp. 465-497. 
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Nagata, Makoto. A generalization of the sizes of differential equations and its applications to $G$-function theory. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 30 (2001) no. 2, pp. 465-497. http://archive.numdam.org/item/ASNSP_2001_4_30_2_465_0/

[1] Y. André, "G-functions and Geometry", Max-Planck-Institut, Bonn, 1989. | MR | Zbl

[2] A. Baker, "Transcendental Number Theory", Cambridge University Press, Cambridge, 1975. | MR | Zbl

[3] E. Bombieri, On G-functions, Recent progress in analytic number theory 2 Academic Press, New York (1981), 1-67. | MR | Zbl

[4] G. Christol - B. Dwork, Differential modules of bounded spectral norms, Contemp. Math. 133 (1992), 39-58. | MR | Zbl

[5] G. Christol - B. Dwork, Effective p-adic bounds at regular singular points, Duke Math. J. 62 (1991), 689-720. | MR | Zbl

[6] D.V. Chudnovsky - G.V. Chudnovsky, Applications of Padé approximations to diophantine inequalities in values of G-functions, Lect. Notes in Math. 1135, Springer-Verlag, Berlin, Heidelberg, New York, (1985), 9-51. | MR | Zbl

[7] G.V. Chudnovsky, On applications of diophantine approximations, Proc. Nat. Acad. Sci. U.S.A. 81 (1984), 1926-1930. | MR | Zbl

[8] B. Dwork - G. Gerotto - F.J. Sullivan, "An Introduction to G-functions", Annals of Math. Studies 133 (1994), Princeton University Press, Princeton, New Jersey. | MR | Zbl

[9] A.I. Galo, "Estimates from below of polynomials in the values of analytic functions of a certain class", Math. USSR Sbornik 24 (1974), 385-407, Original article in Math. Sbornik 95 (137) (1974), 396-417. | Zbl

[10] X. Guangshan, On the arithmetic properties of G-functions, International symposium in memory of Hua Loo Keng (Number theory) 1 (1991), Springer-Verlag, Berlin, Heidelberg, New York, 331-346. | MR | Zbl

[11] K. Mahler, "Lectures on Transcendental Numbers", Lect. Notes in Math. 546 (1976), Springer-Verlag, Berlin, Heidelberg, New York. | MR | Zbl

[12] K. Mahler, Perfect systems, Compositio Math. 19 (1968), 95-166. | Numdam | MR | Zbl

[13] M. Nagata, Sequences of differential systems, Proc. Amer. Math. Soc. 124 (1996), 21-25. | MR | Zbl

[14] A.B. Shidlovskii, "Transcendental Numbers", Walter de Gruyter, Berlin, New York, 1989. | MR | Zbl

[15] K. Väänänen, On linear forms of a certain class of G-functions and p-adic G-functions, Acta Arith. 36 (1980), 273-295. | MR | Zbl

[16] C.L. Siegel, "Über einige Anwendungen diophantischer Approximationen ", Abh. Preuss. Akad. Wiss., Phys. Math. Kl. nr.1 (1929). | JFM